Cubic packing

An unusual crystal arrangement is exhibited by the isomorphous compounds CrCl and Crl. The close-packed cubic array of Cl or I atoms has two-thirds of the octahedral holes between every other pair of chlorine or iodine planes filled with chromium atoms. Alternate layers of the halogen compounds are held together by van der Waals forces (39,40). 

Compounds that have the empirical formulas MCr02 and DCr204 where M is a monovalent and D a divalent cation, are known as chromites. These are actually mixed oxides and probably are better written as M20-Cr203 and D0-Cr203, respectively. The oxides of D are largely spinels, ie, the oxygen atoms define a close-packed cubic array having the octahedral holes occupied by the Cr(III) cation and the tetrahedral holes occupied by D (54). Chromite ore is an important member of this class of oxides. 

Ziegler-Natta catalyst A stereospecific catalyst for polymerization reactions, consisting of titanium tetrachloride and triethylaluminum. zinc-blende structure A crystal structure in which the cations occupy half the tetrahedral holes in a nearly close packed cubic lattice of anions also known as sphalerite structure. 

This completes our discussion of the beisis and factors developed by past investigators to describe and conceptulize the structure of solids. You will note that we have not yet fully described the s)unmetry factor of solids. The reason for this is that we use symmetry factors to characterize solid structure without resorting to the theoretical basis of structure determination. That is, we have a standard method for categorizing solid structures. We say that salt, NaCl, is cubic. That is, the Na" ion and the Cl ion are alternately arranged in a close-packed cubic structure. The next section now investigates these structure protocols. 

Horse-spleen apoferritin crystallizes in a face-centred, close-packed, cubic arrangement, in the space group F432, with molecules at the 432 symmetry points of the crystal lattice (Harrison, 1959). This publication was the logical extension of the DPhil thesis of the Oxford chemist Pauline M. Cowan (as she was before her marriage to Roy Harrison), and represented the first publication in what was to be a long and distinguished series of contributions on ferritin from the undisputed Iron Lady of iron metabolism. ... 

The surface lattice plane of Pt (lOO)-(l x 1), created by cleavage along the close-packed cubic lattice plane (100) of platinum crystals, transforms into the... 

White lustrous metal when freshly prepared turns silvery exists in two forms as a double hexagonal closed-packed alpha form, and a closed-packed cubic structure known as beta form melts at 994°C more volatile than its neighbor elements, plutonium or curium vaporizes at 2,607°C density 13.67 g/cm soluble in dilute acids. 

Silvery-white metal close-packed cubic crystals lattice constant 3.8394A at 20°C density 22.42 g/cm (highest among metals) melts at 2410°C vaporizes at 4,130°C hardness 6-6.5 Mohs electrical resistivity 4.71 j,ohm-cm Young s modulus 3.75 x 10 tons/in magnetic susceptibility 0.133 x 10 cm3/g thermal neutron absorption cross section 440 barns. 

Figure 1.41) have the oxygen ions in a nearly close-packed cubic array. The unit cell contains 32 oxygen ions, with 32 octahedral and 64 tetrahedral sites, of which 16 of the octahedral and 8 of the tetrahedral sites are filled. It is the position of these 24 cations within the unit cell that determines magnetic behavior. The distribution of cations in the sites is specific to the type of cations, and it must be determined experimentally. There are two idealized spinel structures. In the normal spinel, all the divalent ions are on the tetrahedral sites, as in ZnFe204. In the inverse spinel, the 8 occupied tetrahedral sites are filled with trivalent ions and the 16 occupied octahedral sites are equally divided between di- and trivalent ions (see Figure 6.63). The prototypical inverse spinel ferrite is magnetite, whose structure consists of an FCC oxygen array with Fe + and Fe + ions in the interstices.

The concept of close packing is particularly useful in describing the crystal structures of metals, most of which fall into one of three classes hexagonal close packed, cubic close packed (i.e., fee), and body-centered cubic (bcc). The bcc unit cell is shown in Fig. 4.8 its structure is not close packed. The stablest structures of metals under ambient conditions are summarized in Table 4.1. Notable omissions from Table 4.1, such as aluminum, tin, and manganese, reflect structures that are not so conveniently classified. The artificially produced radioactive element americium is interesting in that the close-packed sequence is ABAC..., while one form of polonium has... 

Fig. 7.77. Three crystallographic arrangements as seen for the dose-packed cubic lattice of silver.

Hexagonal closest packing Cubic closest packing... 

To simplify our calculations, let us define a reference lattice by assuming that the shape of a chromophore can be approximated as an ellipsoid (see Fig. 10). Taking the long axis of the ellipse as 10, we can define a closely packed cubic lattice of spheres of diameter 10. The number density associated with this lattice is N0=(l0) 3. For chromophore concentrations (loading in a host matrix) below this reference number density (i.e., N=N0x lattice with lattice constant, a=b=(N0) 1/3(x) l/3. For N >N0, only the intermolecular distances in the plane perpendicular to the principle ellipsoid axis can decrease with increasing concentration, x. We have a simple tetrahedral lattice with lattice constants, a=(N0) 1/3(x) l/3 b=(N0) l/3. 

Solute atoms, which are smaller than the solvent atoms in binary interstitial alloys, such as C, H, N, and O are usually incorporated as interstitials in the void sites of the lattice, for example, in octahedral and tetrahedral sites in the close-packed cubic and close-packed hexagonal lattices (see Figures 1.6, 1.7, and 2.12), and in the body-centered cubic lattices (Figure 5.9) [7],... 

Thermogravimetric analysis of nickel(II) chloride hexa-hydrate shows that water evolution occurs from ambient temperatures (25°) to 66.6°. The resulting dihydrate is stable up to 133.3°, beyond which temperature further water loss occurs. Differential thermal analysis shows an endotherm at 53.9° related to the first dehydration step, and a second, strong endotherm at 118.9°, not accompanied by any weight loss, indicates the transformation of an octahedrally coordinated to a close-packed cubic structure. 

Figure 6.1 Common crystal structures in ceramics (a) Simple cubic (or CsCl) structure (b) close-packed cubic (or NaCl), a variant of the face centered cubic (FCC) structure (c) hexagonal close-packed (HCP).

Close packed cubic. This is also called the NaCl structure and is really a variant of the face centered cubic (FCC) structure. Examples of this structure include CaO, MgO, MnO, NiO, FeO and BaO. Oxygen ions occupy the FCC positions while the metal ions occupy the interstices. 

Normal spinet has a close-packed cubic laitice of oxygen ions, The caiions are situated in tetrahedral (A) or octahedral (B) sites and their ratio in the unit ceil corresponds to the formula AB2O4. 

Solve the equation 4r = 72 (142) pm r = 50.2 pm (b) The radius of is 133 pm. In close-packed cubic unit cell (face-centered cubic unit cell), the tetrahedral holes are smaller than the octahedral holes. The sizes of tetrahedral holes can be calculated as follows One unit cell can be divided into eight subunit cells and each subunit cell contains one tetrahedral hole. The face diagonal of each... 

From these results and Example 3.3, it becomes clear that closed-packed cubic lattice has the best space economy (best packing, least empty space), followed by the body-centred lattice, whereas the simple cubic packing has the lowest space economy with the highest fraction of unoccupied space. 

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